Guessing secrets.
How Long Can One Bluff in the Domination Game?
The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established. minus graphs...
How to play MetaSquares
Infinite asymptotic games
We study infinite asymptotic games in Banach spaces with a finite-dimensional decomposition (F.D.D.) and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bases and Banach spaces. The results are related to questions of rapidity...
Infinite -games with imperfect information
Information-theoretical optimization techniques
Interval valued bimatrix games
Payoffs in (bimatrix) games are usually not known precisely, but it is often possible to determine lower and upper bounds on payoffs. Such interval valued bimatrix games are considered in this paper. There are many questions arising in this context. First, we discuss the problem of existence of an equilibrium being common for all instances of interval values. We show that this property is equivalent to solvability of a certain linear mixed integer system of equations and inequalities. Second, we...
Introduction to the “prisoners and guards” game.
Jeu de Choquet
Jeux quantitatifs [Book]
Juegos invariantes.
Juegos que presentan ciertas propiedades de simetría respecto a grupos de transformaciones son reducidos a un juego restringido. Se demuestra que si el grupo es transitivo, el juego tiene valor. El análisis armónico nos permite caracterizar las estrategias óptimas.
Juegos sobre conjuntos finitos sin estructura.
En este trabajo estudiamos algunos juegos en los que las estrategias son subconjuntos de un conjunto finito y la función de pago depende de los cardinales de dichas estrategias.Para resolver estos juegos resolvemos previamente un juego auxiliar.Presentamos un esquema que muestra la relación de dependencia que existe entre los juegos tratados.
King and rook vs. king on a quarter-infinite board.
Linear complementarity problems and bi-linear games
In this paper, we define bi-linear games as a generalization of the bimatrix games. In particular, we generalize concepts like the value and equilibrium of a bimatrix game to the general linear transformations defined on a finite dimensional space. For a special type of -transformation we observe relationship between the values of the linear and bi-linear games. Using this relationship, we prove some known classical results in the theory of linear complementarity problems for this type of -transformations....
Linear-quadratic differential games: from finite to infinite dimension
The object of this paper is the generalization of the pioneering work of P. Bernhard [J. Optim. Theory Appl. 27 (1979)] on two-person zero-sum games with a quadratic utility function and linear dynamics. It relaxes the semidefinite positivity assumption on the matrices in front of the state in the utility function and introduces affine feedback strategies that are not necessarily L²-integrable in time. It provides a broad conceptual review of recent results in the finite-dimensional case for which...
Minimaxtheoreme und das Integraldarstellungsproblem.
Mixed complementarity problems for robust optimization equilibrium in bimatrix game
In this paper, we investigate the bimatrix game using the robust optimization approach, in which each player may neither exactly estimate his opponent’s strategies nor evaluate his own cost matrix accurately while he may estimate a bounded uncertain set. We obtain computationally tractable robust formulations which turn to be linear programming problems and then solving a robust optimization equilibrium can be converted to solving a mixed complementarity problem under the -norm. Some numerical...
Mr. Paint and Mrs. Correct.
Nash Equilibria in a class of Markov stopping games
This work concerns a class of discrete-time, zero-sum games with two players and Markov transitions on a denumerable space. At each decision time player II can stop the system paying a terminal reward to player I and, if the system is no halted, player I selects an action to drive the system and receives a running reward from player II. Measuring the performance of a pair of decision strategies by the total expected discounted reward, under standard continuity-compactness conditions it is shown...
New games related to old and new sequences.